Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x - 8$ and $ BC = 6x + 19$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x - 8} = {6x + 19}$ Solve for $x$ $ 3x = 27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({9}) - 8$ $ BC = 6({9}) + 19$ $ AB = 81 - 8$ $ BC = 54 + 19$ $ AB = 73$ $ BC = 73$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {73} + {73}$ $ AC = 146$